Comparative analysis of energy-level splitting of Pr^(3+) doped in LiYF_4 and LiBiF_4 crystals:a complete energy matrix calculation

摘要

Based on the combination of Racah's group-theoretical consideration with Slater's wavefunction,a 91×91 complete energy matrix is established in tetragonal ligand field D 2d for Pr 3+ ion.Thus,the Stark energy-levels of Pr 3+ ions doped separately in LiYF 4 and LiBiF 4 crystals are calculated,and our calculations imply that the complete energy matrix method can be used as an effective tool to calculate the energy-levels of the systems doped by rare earth ions.Besides,the influence of Pr 3+ on energy-level splitting is investigated,and the similarities and the differences between the two doped crystals are demonstrated in detail by comparing their several pairs of curves and crystal field strength quantities.We see that the energy splitting patterns are similar and the crystal field interaction of LiYF 4:Pr 3+ is stronger than that of LiBiF 4:Pr 3+.